Reprocessing in Luminous Disks

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Abstract
We develop and investigate a procedure that accounts for disk reprocessing of photons that originate in the disk itself. Surface temperatures and simple, blackbody spectral energy distributions (SEDs) of protostellar disks are calculated. In disks that flare with radius, reprocessing of stellar photons results in temperature profiles that are not power-law at all radii but are consistently shallower than r-3/4. Including the disk as a radiation source (as in the case of active accretion) along with the stellar source further flattens the temperature profile. Disks that flare strongly near the star and then smoothly curve over and become shadowed at some distance ("decreasing curvature" disks) exhibit nearly power-law temperature profiles that result in power-law infrared SEDs with slopes in agreement with typical observations of young stellar objects. Disk models in which the photospheric thickness is controlled by the local opacity and in which the temperature decreases with radius naturally have this shape. Uniformly flaring models do not match observations as well; progressively stronger reprocessing at larger radii leads to SEDs that flatten toward the infrared or even have a second peak at the wavelength corresponding (through the Wien law) to the temperature of the outer edge of the disk. In FU Orionis outbursting systems, the dominant source of energy is the inner disk. Reprocessing throughout the disk depends sensitively on the inner disk shape and emitted temperature profile. We show that the thermal instability outburst models of Bell & Lin reproduce trends in the observed SEDs of FU Ori systems with T ∝ r-3/4 in the inner disk (r 0.25 AU corresponding to λ 10 μm) and T ∝ r-1/2 in the outer disk. Surface irradiation during outburst and quiescence is compared in the region of planet formation (1-10 AU). The contrast between the two phases is diminished by the importance of the reprocessing of photons from the relatively high mass flux, outer disk ( = 10-5 M☉ yr-1), which is present during both outburst and quiescence.